If you're interested in which will perform better, you need to test it on the target platform. Nothing in the standard mandates how the functions are implemented and, while it may seem logical that a non-checking memcpy would be faster, this is by no means a certainty.
It's quite possible, though unlikely, that the person who wrote memmove for your particular compiler was a certified genius while the poor soul who got the job of writing memcpy was the village idiot :-)
Although, in reality, I find it hard to imagine the memmove could be faster than memcpy, I don't discount the possibility. Measure, don't guess.